The research of high accuracy and high resolution schemes have been a hot topic in computationalmathematics． According to low resolution and large amount of calculation of the original WENO-JS scheme，wepropose a simple new limiter fifth order upwind WENO scheme to reconstruct the numerical flux of the simplestructure to improve the computational efficiency． Compared with other efficient high accuracy schemes such asENO and WENO，it is shown that the computational cost of this scheme is less than that of WENO-JS in the sameaccuracy． By use of MATLAB software，we compared and analyzed computational efficiencies and computationalaccuracies of Lax-Wendroff WENO-JS scheme，Lax-Wendroff simple limiter WENO scheme，Ｒunge-Kutta simplelimiter WENO scheme and Ｒunge-Kutta WENO-JS scheme． The numerical results show that the new Lax-Wendroffsimple limiter WENO scheme can improve the computing speed and reduce the computing time by 20% whilemaintaining the original WENO resolution